document.write( "Question 1203149: The cost of two chairs and three tables for an office is $1,800.00. After a month, the cost of each chair and each table increased by 20%. The office again bought 6 chairs and 2 tables at $4,800.00. Calculate the new cost of a chair and a table. \n" ); document.write( "

Algebra.Com's Answer #838482 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "The cost of two chairs and three tables for an office is $1,800.00.
\n" ); document.write( "After a month, the cost of each chair and each table increased by 20%.
\n" ); document.write( "The office again bought 6 chairs and 2 tables at $4,800.00.
\n" ); document.write( "Calculate the new cost of a chair and a table.
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document.write( "Let x be the cost of a chair previous month; y be the cost of a table previous month.\r\n" );
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document.write( "Then the purchase equation for the previous month is\r\n" );
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document.write( "    2x + 3y = 1800  dollars.    (1)\r\n" );
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document.write( "Next month the cost of a chair is 1.2x; the cost of a table is 1.2y.\r\n" );
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document.write( "Next month purchase equation is\r\n" );
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document.write( "    6*(1.2x) + 2*(1.2y) = 4800  dollars.    (2)\r\n" );
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document.write( "Transform equation (2) by dividing all its terms by 1.2. You will get\r\n" );
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document.write( "    6x + 2y = 4000.    (3)\r\n" );
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document.write( "Thus we have a system of two equations\r\n" );
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document.write( "    2x + 3y = 1800     (1')\r\n" );
document.write( "    6x + 2y = 4000     (3')\r\n" );
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document.write( "To solve, multiply equation (1') by 3; keep equation (3') as is\r\n" );
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document.write( "    6x + 9y = 5400     (1'')\r\n" );
document.write( "    6x + 2y = 4000     (3'')\r\n" );
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document.write( "From equation (1'') subtract equation (3'').  You will get\r\n" );
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document.write( "         9y - 2y = 5400 - 4000\r\n" );
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document.write( "            7y   =    1400\r\n" );
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document.write( "             y   =    1400/7 = 200.\r\n" );
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document.write( "Thus one table cost was 200 dollars previous month;  \r\n" );
document.write( "so next month new price is 1.2*200 = 240 dollars per table. \r\n" );
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document.write( "Now from equation (1),\r\n" );
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document.write( "    2x + 3*200 = 1800,  2x = 1800 - 3*200 = 1200,  x = 1200/2 = 600 dollars.\r\n" );
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document.write( "Thus one chair cost was 600 dollars previous month;\r\n" );
document.write( "so next month new price is 1.2*600 = 720 dollars per chair.\r\n" );
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document.write( "ANSWER.  New prices are 240 dollars per table and 720 dollars per chair.\r\n" );
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